Church’s Theorem and the Analytic-Synthetic distinction in Mathematics

Por • 13 ago, 2018 • Sección: Educacion

Charles Castonguay

” Kant’s classification of mathematical truth as synthetic a priori has given rise to a very considerable literature on the subject. We will limit ourselves here to discussing a recent attempt to vindicate Kant in terms of certain results in contemporary first order logic. In a series of letures delivered at Oxford in the early sixties, J. Hintikka has proposed formal explications of the Kantian distinction between analytic and synthetic truths and arguments. Entitled “An Analysis of Analyticity”, “Are Logical Truths Tautologies? “, “Kant Vindicated”, and “Kant and the Tradition of Analysis”, these lectures now form a central part of Hintikka’s book Logic, Language Games and Infom1ation Kantian Themes in the Philosophy of Logic(Oxford, 1973); henceforth references to Hintikka’s presentation will simply be given by the appropriate page number in the book. We shall first give an overview of Hintikka’s arguments, then examine then criticallly, and finally argue for Church’s Theorem as a superior formal vindication of Kant’s position.

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